2(u+1)5u=3(u+1)-2

Solution for 2(u+1)5u=3(u+1)-2 equation:

Simplifying
2(u + 1) * 5u = 3(u + 1) + -2

Reorder the terms:
2(1 + u) * 5u = 3(u + 1) + -2

Reorder the terms for easier multiplication:
2 * 5u(1 + u) = 3(u + 1) + -2

Multiply 2 * 5
10u(1 + u) = 3(u + 1) + -2
(1 * 10u + u * 10u) = 3(u + 1) + -2
(10u + 10u2) = 3(u + 1) + -2

Reorder the terms:
10u + 10u2 = 3(1 + u) + -2
10u + 10u2 = (1 * 3 + u * 3) + -2
10u + 10u2 = (3 + 3u) + -2

Reorder the terms:
10u + 10u2 = 3 + -2 + 3u

Combine like terms: 3 + -2 = 1
10u + 10u2 = 1 + 3u

Solving
10u + 10u2 = 1 + 3u

Solving for variable 'u'.

Reorder the terms:
-1 + 10u + -3u + 10u2 = 1 + 3u + -1 + -3u

Combine like terms: 10u + -3u = 7u
-1 + 7u + 10u2 = 1 + 3u + -1 + -3u

Reorder the terms:
-1 + 7u + 10u2 = 1 + -1 + 3u + -3u

Combine like terms: 1 + -1 = 0
-1 + 7u + 10u2 = 0 + 3u + -3u
-1 + 7u + 10u2 = 3u + -3u

Combine like terms: 3u + -3u = 0
-1 + 7u + 10u2 = 0

Begin completing the square.  Divide all terms by
10 the coefficient of the squared term: 

Divide each side by '10'.
-0.1 + 0.7u + u2 = 0.0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 0.7u + 0.1 + u2 = 0.0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 0.7u + u2 = 0.0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 0.7u + u2 = 0.0 + 0.1
0.7u + u2 = 0.0 + 0.1

Combine like terms: 0.0 + 0.1 = 0.1
0.7u + u2 = 0.1

The u term is 0.7u.  Take half its coefficient (0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
0.7u + 0.1225 + u2 = 0.1 + 0.1225

Reorder the terms:
0.1225 + 0.7u + u2 = 0.1 + 0.1225

Combine like terms: 0.1 + 0.1225 = 0.2225
0.1225 + 0.7u + u2 = 0.2225

Factor a perfect square on the left side:
(u + 0.35)(u + 0.35) = 0.2225

Calculate the square root of the right side: 0.471699057

Break this problem into two subproblems by setting 
(u + 0.35) equal to 0.471699057 and -0.471699057.

Subproblem 1
u + 0.35 = 0.471699057

Simplifying
u + 0.35 = 0.471699057

Reorder the terms:
0.35 + u = 0.471699057

Solving
0.35 + u = 0.471699057

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-0.35' to each side of the equation.
0.35 + -0.35 + u = 0.471699057 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + u = 0.471699057 + -0.35
u = 0.471699057 + -0.35

Combine like terms: 0.471699057 + -0.35 = 0.121699057
u = 0.121699057

Simplifying
u = 0.121699057

Subproblem 2
u + 0.35 = -0.471699057

Simplifying
u + 0.35 = -0.471699057

Reorder the terms:
0.35 + u = -0.471699057

Solving
0.35 + u = -0.471699057

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-0.35' to each side of the equation.
0.35 + -0.35 + u = -0.471699057 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + u = -0.471699057 + -0.35
u = -0.471699057 + -0.35

Combine like terms: -0.471699057 + -0.35 = -0.821699057
u = -0.821699057

Simplifying
u = -0.821699057

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.121699057, -0.821699057}